1. Sisyphus cooling and pumping of linear oscillator by superconducting qubit
M. Grajcar
Comenius University, Slovakia
A. Izmalkov, S.H.W. van der Ploeg, Th. Wagner, E. I’lichev, H.-G. Meyer
Institute for Physical High Technology, Germany
A. Fedorov, A. Shnirman, Gerd Schön,
Institut für Theoretische Festkörperphysik Universität
Karlsruhe, Germany
S.N. Shevchenko, A.N. Omelyanchouk,
B.Verkin Institute for Low Temperature Physics and Engineering,
Kharkov, Ukraine
S. Ashhab, J.R. Johansson, A. Zagoskin and Franco Nori,
The Institute of Physical and Chemical Research (RIKEN),
Wako-shi, Japan

2. Outline Superconducting flux qubit
Adiabatic measurement of the qubit in the ground state
Spectroscopic measurement
Sisyphus cooling and pumping
Lower limit on the achievable temperature

3. Single-junction interferometer (RF-SQUID)1
Or in normalized Units:
Classical two level System!

4. Classical picture 1  p 2p f
Particle with mass ~ CJ in potential:

5. Quantum Picture d p 2p f
If CJ is small enough tunneling between both wells becomes possible and therefore the degeneracy is lifted.
So we need Small Josephson Junctions with EJ/EC~10-100

6. Persistent current (flux) qubit – analogue of ammonia moleculenF B
Superconducting persistent current qubit – oscillation of
a magnetic dipole moment (magnetic flux),
Ammonia molecule – oscillation of an electric dipole moment
(f=24 GHz) N H + + H + H

7. Size problem and solution
For quantum behavior
EJ/EC~10-100
Typical parameters for aluminum technology :

8. Solution of the size problem
‚Size‘ problem solved in 70´s
T. Yamashita et al., J. Appl. Phys. 50, 3547 (1979)
This idea was dusted off by
J.E. Mooij et al., Science 285, 1036, 1999

9. Hamiltonian. Energy surface.

10. Tunneling amplitude   GHz -0 0 E0
ЕС=5 GHz, g=EJ/EC=66, ЕJ=330 GHz. 
0.85
0.86
0.87
0.88
0.89
0.9
0.901
0.902
0.905
0.91
0.92 
GHz 20 13
8.45
5.44
3.49
2.24
2.14
2.05
1.79
1.43

11. Pseudospin Hamiltonian
IC, f2
IC, f1
aIC
(0.5<a<1) Fx
1 um

12. Flux qubit coupled to oscillatorVT LT L CT Ib M

13. Adiabatic measurement away from degeneracy point

14. Adiabatic measurement at degeneracy point

15. Lagrangian of the qubit-resonator system
Expanding into Taylor series up to the second order term 2

16. Φi Quantum approach C L L I is satisfied. At the degeneracy point b
No perturbation of the measured observable [V.B. Braginsky and F.Ya. Khalili, Quantum Measurement, (Cambridge University Press, Cambridge, 1992].
The sufficient condiction for Quantum Nondemolition Measurements
is satisfied.

17. Impedance Measurement, classical resonatorLT L CT Φ VT Ib
Build a resonator, connect something to it with a susceptibility different from zero and it will change its resonant frequency.
Ya. S. Greenberg et al., PRB 66, (2002)
DC-Squid Josephson Inductance: A. Lupascu et al., PRL 93, (2004).

18. Response of resonator   GHz EJ/Ec<102 =0.9 EJ/Ec103
=0.8 
0.86
0.88
0.9
0.901
0.902
0.905
0.91
0.92
 GHz 13
5.44
2.24
2.14
2.05
1.79
1.43

19. Resonant frequency of the resonator
Y. Greenberg et al., PRB 66
(2002).
Fitting parameters

20. Sisyphus work Greek mythology
As a punishment from the gods for his trickery, Sisyphus was compelled
to roll a huge rock up a steep hill, but before he reached the top of the hill,
the rock always escaped him and he had to begin again.
Titian (1549) artist vision of Sisyphus work
Physical realization:
For atoms
D. J. Wineland, J. Dalibard and C. Cohen-Tannouji, J.
Opt. Soc. B9, 3242 (1992).
For qubit
Grajcar et al., arXiv:
Nature Physics 4, (2008).

21. Sisyphus cooling

22. Sisyphus pumping

23. Adiabatic vs. spectroscopic measurement
Solid line is theoretical curve for
Parameters determined from adiabatic
measurement

24. Strong microwave driving at fmw=4.5 GHz
Strong driving
Transition from weak to strong driving
Weak driving
dc (0)
A. Izmalkov et al., PRL 101, (2008)
W.D. Oliver et al.,SCIENCE 310, 1653(2005)
M. Sillanpää et al., PRL 96, (2006)

25. Landau-Zener interferometry
A.V. Shytov, D.A. Ivanov, and M.V. Feigel’man, Eur. Phys. J. B 36, 263 (2003).
S.N. Shevchenko et al. Phys. Rev. B 78, (2008)

26. More rigorous treatment of Sisyphus cooling/pumping
A. Fedorov, A. Shnirman, Gerd Schön
fmw=14 GHz
M. Grajcar et al.,
Nature Physics 4,
(2008).

27. Spectral density of the voltage noise of the tank
fmw=8 GHz

28. Tank circuit coupled to mechanical oscillator

29. Sisyphus and sideband cooling limit
M. Grajcar, A. Ashhab, J.R. Johansson, F. Nori
Phys. Rev. B 78, (2008)

30. Conclusions
Superconducting flux qubits are well described by two-level (pseudospin) Hamiltonian
Experimental data obtained from adiabatic and spectroscopic measurement are consistent and fully agree with the quantum-mechanical predictions to the experimental accuracy.
The qubit can be used as an artificial atom for Sisyphus cooling of a low frequency oscillator (electrical, nanomechanical, etc.)

31. Ground state energy modulation -  + - +
m= -1/2
m= 1/2

32. Sisyphus cooling

33. Design for spectroscopic measurement

34. Spectroscopy of the system of two coupled flux qubits.
A. Izmalkov et al., PRL 101, (2008)
Without microwave driving
fmw= 14 GHz
fmw= 18 GHz
fmw= 21 GHz

35. Nanomechanical oscillators
Nanobridge from IPHT Jena
Neik et al., Nature 443, (2006)
I. Martin, A. Shnirman, Lin Tian, P. Zoller
Ground state cooling of mechanical resonators
Phys. Rev. B 69, (2004)
Prepared for measurement at
temprature below1 mK in ulra low
temp. lab in Košice

36. Quantum metamaterials
Design of high efficiency microwave photon detector for GHz range
G. Romero et al., Microwave Photon Detector in Circuit QED, arXiv: v1

37. Four qubit sample q3 q1 q4 q2 Layout Micrograph A3 Iq3 Iq1 A2 Ib4 Iq2

38. Anti-Ferromagnetic and Ferromagnetic Coupling
AFM FM
Iq2=-10 µA
Iq3=0
Iq4=-250 µA

39. Theoretical fits. Phys. Rev. Lett. 96, 047006 (2006)
Experiment
Theory

40. Psedo-spin Hamiltonian